Mathematical Sciences: Analytic and Algebraic Methods in Geometry and Number Theory

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This award supports the research in automorphic forms and representations of Professor Goro Shimura of Princeton University. Dr. Shimura's work will be concerned principally with the topics of: the periods of automorphic forms of arithmetic type; differential operators on symmetric spaces; and the special values of various zeta functions and Eisenstein series. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of modular and automorphic forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots.